4,020 research outputs found
A simple proof of Perelman's collapsing theorem for 3-manifolds
We will simplify earlier proofs of Perelman's collapsing theorem for
3-manifolds given by Shioya-Yamaguchi and Morgan-Tian. Among other things, we
use Perelman's critical point theory (e.g., multiple conic singularity theory
and his fibration theory) for Alexandrov spaces to construct the desired local
Seifert fibration structure on collapsed 3-manifolds. The verification of
Perelman's collapsing theorem is the last step of Perelman's proof of
Thurston's Geometrization Conjecture on the classification of 3-manifolds. Our
proof of Perelman's collapsing theorem is almost self-contained, accessible to
non-experts and advanced graduate students. Perelman's collapsing theorem for
3-manifolds can be viewed as an extension of implicit function theoremComment: v1: 9 Figures. In this version, we improve the exposition of our
arguments in the earlier arXiv version. v2: added one more grap
Hawking Radiation from Feynman Diagrams
The aim of this letter is to clarify the relationships between Hawking
radiation and the scattering of light by matter falling into a black hole. To
this end we analyze the S-matrix elements of a model composed of a massive
infalling particle (described by a quantized field) and the radiation field.
These fields are coupled by current-current interactions and propagate in the
Schwarzschild geometry. As long as the photons energy is much smaller than the
mass of the infalling particle, one recovers Hawking radiation since our
S-matrix elements identically reproduce the Bogoliubov coefficients obtained by
treating the trajectory of the infalling particle classically. But after a
brief period, the energy of the `partners' of Hawking photons reaches this mass
and the production of thermal photons through these interactions stops. The
implications of this result are discussed.Comment: 12 pages, revtex, no figure
From Vacuum Fluctuations to Radiation: Accelerated Detectors and Black Holes
The vacuum fluctuations that induce the transitions and the thermalisation of
a uniformly accelerated two level atom are studied in detail. Their energy
content is revealed through the weak measurement formalism of Aharonov et al.
It is shown that each time the detector makes a transition it radiates a
Minkowski photon. The same analysis is then applied to the conversion of vacuum
fluctuations into real quanta in the context of black hole radiation. Initially
these fluctuations are located around the light like geodesic that shall
generate the horizon and carry zero total energy. However upon exiting from the
star they break up into two pieces one of which gradually acquires positive
energy and becomes a Hawking quantum, the other, its ''partner", ends up in the
singularity. As time goes by the vacuum fluctuations generating Hawking quanta
have exponentially large energy densities. This implies that back reaction
effects are large.Comment: definitive version, 39 pages and 5 figures available upon request
from S.M., ULB-TH 94/0
The Rotating Quantum Vacuum
We derive conditions for rotating particle detectors to respond in a variety
of bounded spacetimes and compare the results with the folklore that particle
detectors do not respond in the vacuum state appropriate to their motion.
Applications involving possible violations of the second law of thermodynamics
are briefly addressed.Comment: Plain TeX, 10 pages (to appear in PRD
Analytical calculation of the excess current in the OTBK theory
We present an analytical derivation of the excess current in Josephson
junctions within the Octavio-Tinkham-Blonder-Klapwijk theory for both symmetric
and asymmetric barrier strengths. We confirm the result found numerically by
Flensberg et al. for equal barriers [Phys. Rev. B 38, 8707 (1988)], including
the prediction of negative excess current for low transparencies, and we
generalize it for differing barriers. Our analytical formulae provide for
convenient fitting of experimental data, also in the less studied, but
practically relevant case of the barrier asymmetry.Comment: 13 pages, 3 figures, submitted to Superconductor Science and
Technolog
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